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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "004fbd82",
+   "metadata": {},
+   "source": [
+    "# [Pandigital Prime](https://projecteuler.net/problem=41)\n",
+    "\n",
+    "There's only $1! + 2! + 3! + \\cdots + 9! = 409113$ $n$-digit pandigital numbers. This is a small enough number to brute force, but we can easily optimize even further by applying a [divisibility rule](https://en.wikipedia.org/wiki/Divisibility_rule).\n",
+    "\n",
+    "If the digits of a number sum to a multiple of 3, that number is divisible by 3. Since:\n",
+    "* the digits of every 5-digit pandigital number will sum to 15\n",
+    "* the digits of every 6-digit pandigital number will sum to 21\n",
+    "* the digits of every 8-digit pandigital number will sum to 36\n",
+    "* the digits of every 9-digit pandigital number will sum to 45\n",
+    "\n",
+    "all of these numbers will be divisible by 3, and therefore not be prime. Consequently, to find the largest $n$-digit pandigital prime, we only need to check 4-digit and 7-digit pandigital numbers."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9fead48d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from itertools import permutations\n",
+    "\n",
+    "pandigitals = set()\n",
+    "for n in (4, 7):\n",
+    "    for permutation in permutations(range(1, n + 1)):\n",
+    "        k = sum(10^i * d for (i, d) in enumerate(reversed(permutation)))\n",
+    "        pandigitals.add(k)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5a4dd5de",
+   "metadata": {},
+   "source": [
+    "Now just sort largest-to-smallest and find the first prime."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "a6eb3473",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "7652413"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "for p in reversed(sorted(pandigitals)):\n",
+    "    if is_prime(p):\n",
+    "        break\n",
+    "\n",
+    "p"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6a9c043d",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Pandigital numbers: [A352991](https://oeis.org/A352991)\n",
+    "* Pandigital primes: [A216444](https://oeis.org/A216444)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}